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Mixed lump–soliton solutions to the two-dimensional Toda lattice equation via symbolic computation

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Abstract

Based on symbolic computation, we derive explicit rational and rational–exponential solutions to two-dimensional Toda lattice equation via the direct bilinear method. For two types of solutions, the auxiliary functions are taken as the ansatzs with the quadratic function and the combination of quadratic and exponential functions, respectively. It is shown that the purely rational solution depicts a lump with the locality in all directions in the space. The mixed rational–exponential solutions are classified to two kinds of interaction solution: (i) The first one describes the interaction of one lump with one line soliton, in which fission and fusion phenomena occurs between both local waves. (ii) The second one corresponds to the interaction of one lump with two resonant line solitons, which indicates a rogue wave arising from the resonant soliton pair.

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Acknowledgements

This work was supported by the NSF of China under Grant Nos. 11705077 and 11775104, and National College Students’ innovation and entrepreneurship training program (201810352004).

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  1. Department of Mathematics, Institute of Nonlinear Analysis, Lishui University, Lishui, 323000, China

    Li Chen, Junchao Chen & Qiaoyun Chen

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  1. Li Chen
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  2. Junchao Chen
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Correspondence to Junchao Chen.

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Chen, L., Chen, J. & Chen, Q. Mixed lump–soliton solutions to the two-dimensional Toda lattice equation via symbolic computation. Nonlinear Dyn 96, 1531–1539 (2019). https://doi.org/10.1007/s11071-019-04869-y

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